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Calculation of Improper Integrals by Using Uniformly Distributed Sequences

In: Applications of Measure Theory to Statistics

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  • Gogi Pantsulaia

    (Georgian Technical University, Department of Mathematics)

Abstract

A certain modified version of Kolmogorov’s strong law of large numbersStrong law of large numbers is used for an extension of the result of C. Baxa and J. Schoi $$\beta $$ engeier (2002) to a maximal set of uniformly distributed sequences in (0, 1) that strictly contains the set of all sequences having the form $$(\{\alpha n\})_{n \in \mathbf{N}}$$ for some irrational number $$\alpha $$ and having the full $$\ell _1^{\infty }$$ -measure, where $$\ell _1^{\infty }$$ denotes the infinite power of the linear Lebesgue measure $$\ell _1$$ in (0, 1).

Suggested Citation

  • Gogi Pantsulaia, 2016. "Calculation of Improper Integrals by Using Uniformly Distributed Sequences," Springer Books, in: Applications of Measure Theory to Statistics, chapter 0, pages 1-18, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-45578-5_1
    DOI: 10.1007/978-3-319-45578-5_1
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